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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A generalization of Anderson's theorem on unimodal functions


Author: Somesh Das Gupta
Journal: Proc. Amer. Math. Soc. 60 (1976), 85-91
MSC: Primary 26A87; Secondary 52A40
DOI: https://doi.org/10.1090/S0002-9939-1976-0425050-7
MathSciNet review: 0425050
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Abstract: Anderson (1955) gave a definition of a unimodal function on $ {R^n}$ and obtained an inequality for integrals of a symmetric unimodal function over translates of a symmetric convex set. Anderson's assumptions, especially the role of unimodality, are critically examined and generalizations of his inequality are obtained in different directions. It is shown that a marginal function of a unimodal function (even if it is symmetric) need not be unimodal.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0425050-7
Keywords: Unimodal function, convex set, invariance, marginal function, inequalities
Article copyright: © Copyright 1976 American Mathematical Society